142 Chapter 2 Linear Equations and Inequalities Applying Simple Interest Example 4 Jorge wants to save money to buy a car in 5 years. If Jorge needs to have $20,250 at the end of 5 years, how much money would he need to invest in a certificate of deposit (CD) at a 2.5% interest rate? Solution: Step 1: Read the problem. Let P represent the original amount invested. Step 2: Label the variables. Step 3: Write a verbal model. Step 4: Write a mathematical equation. Step 5: Solve the equation. a Original b 1interest2 principal 1total2 P Prt total P P10.0252152 20,250 P 0.125P 20,250 1.125P 20,250 1.125P 1.125 20,250 1.125 P 18,000 The original investment should be $18,000. Step 6: Interpret the results and write the answer in words. Skill Practice 5. Cassandra invested some money in her bank account, and after 10 years at 4% simple interest, it has grown to $7700.What was the initial amount invested? 3. Applications Involving Discount and Markup Applications involving percent increase and percent decrease are abundant in many real-world settings. Sales tax, for example, is essentially a markup by a state or local government. It is important to understand that percent increase or decrease is always computed on the original amount given. In Example 5, we illustrate an example of percent decrease in an application where merchandise is discounted. Applying Percents to a Discount Problem Example 5 After a 38% discount, a used treadmill costs $868 on eBay.What was the original cost of the treadmill? Solution: Step 1: Read the problem. Let x be the original cost of the treadmill. Step 2: Label the variables. Avoiding Mistakes The interest is computed on the original principal, P, not on the total amount $20,250. That is, the interest is P (0.025)(5), not ($20,250)(0.025)(5). Answer 5. The initial investment was $5500.
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